Facing up to Complex Problem by Introducing Fuzzy Logic in Control

Copyright © IFAC Large Scale Systems, Beijing, PRC, 1992

FACING UP TO COMPLEX PROBLEM BY INTRODUCING FUZZY LOGIC IN CONTROL A. Titli LAASICNRS and INSA , 7 Avellue du CalaMI Roche, 3J400 Toulouse , Frallce

Abstract: The paper presents different ways to use fuzzy 10glc in conrrel in order to overcome complexity due to the dlfficulty to modelize some process or to use non Linear, ome varylIlg, constrained models. Different Stnlctures using fuzzy logic are given. The robustness of fuzzy control is emphasized.. Some proposals for fW'ther research end the paper. Keywords : complexity, hierarchy, supervision, fuzzy logic, fuzzy controller, neural network..

lNTRODUcnON

In the automatic control field complexity has been for long time characterized by a large amount of variables intervening In conventional mathematical models, often linear ones (Theory of Large Scale Systems - 1965 - 1985 - with the concibution of Mesarovic, Silju, Singh, Titli, lamshidi and others).

In this paper, we will focus our attention on fuzzy contrOl (which is a speciallcind of real time expert system). The rest of the paper is divided as follows : in the first pan, we present the concept of integrated automation of complex system, focussing on the problems for which fuzzy lOgiC can be introduced with benefit.

Later on, complexity meant lack of hlowledge on the parameters of the Large Scale models:

The use of fuzzy logic for the design of fuzzy conrrellers is more detailed in the second pan.

- lack of knowledge about the numerical value of parameters, the sign of them being only known (this corresponds to the Qualitative System Analysis CL. Trave-Massuyes and al.- 1990-)

In a third pan, different simulation with fuzzy con trollers are presented and more general and real applications are evocated.

- lack of knowledge about sign and numerical values of parameters, only the position, in the matrices of the models , of non zero parameters being known (this corresponds to the Structural System Analysis - KJ . Reinschke ( 1988).

A conclusion gives some insights on important topics for more convencing applications. INTI:GRA TED AlITOMAnON OF COMPLEX SYSTEMS

Nowadays complexity means global objectives like regulation and production planning, and supervision, and diagnosis, and reconfigurations, and man-machine cooperation on the same process, by designing and implementing hierarchical (multilevel) StruCTUre.

The differeD! layers of the intewted conQ'Q1 The management of complex systems is more and more important in our technolOgical world. Efficient management means nowadays integrated automation (Fig. 1) including, in a computerised wav, classical cono-ol functions like sequential co~trol, regUlation, optimisation and supervisory tasks for production planning, preventive maintenance, diagnosis (detection of an incident, localisation, explanation and decision : reconfiguration of the control, curative maintenance). These functions are implemented on diso-ibuted or multilevel data·processing systems including data bases and establishing cooperation and dialogue with human decision makers.

Complexity means too presence of phenomena
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Concerning the control functions. large scale systems are often characterized by a large number of variables and a special mternal structure under the form of interconnected sub-systems. ThIS decomposition -into interconnected sub-systemsis sometime obvious or can be deduced through two Steps:

Fig. 2 - Preventive maintenance strategy Is this kind of approach. it is imponant to estimate parameters which have physical meaning hke galn. time constant, etc ... on conunuous process.

- data analvsis of the complex systems using mathematicaJ tools like statistical tools. or better. informational tools. - structural analysis through a graph representation of the complex systems followed by a decomposition or a partition of the corresponding graph.

Then it is necessary to estimate parameters directly on continuous models since the physical meaIllng of the parameters is lost by discretisation. The philosophy is to apply . adequate transformations on continuous dlfferentlal equations (model of the process under study) in order to be able to use least squares (or similar) methods to estimate continuous parameters. Different possibilities are :

Then. a hierarchical-multilevel-contrOl (distributed control units coordinated by upper levels) can be implemented on the inte~connected systems or a decentralised control (distributed control urutS without coordination). For optimal control. an efficient therory is available for the desi~~ of hierarchical structures Le. decomposltloncoordination in caleu :us of variations or in maximum principle. f-.)f de~entralised control (interesting for geographically dlStrJbut.ed systems) additional theoretical difficulties. anse concerning the existence of such a control. hnked for linear systems with the concept of fixed modes. When one is sure about the eXistence of decentralised laws. this control can be computerised in a parametric way using mathematical programming. Unfonunately. thIS problem cannot be decomposed according to the spatial internal structure of the global system.

- Introduction of low-pass filter-<>perators - Introduction of a decomposition of the signals on a basis of onhogonal functions (Legencire. Leguerre, ... ). Dia~osis

By a continuous inspection of the data available on the process, we proceed in two steps: - off line learning on the behaviour of the process (by simulation for example) in order to define different classes of functionning. - on Line classification of the current data comlng from the process in one of the different classes. Decision on the basis of this classification.

Furthermore. at this control level. some considerations about robusOless can be introduced to malee the contrOl less sensitive to parameter and/or structural penurbations. Sypenisjon in

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Available tools are data analysis. pattern recognition, classification methods but also parameter estimation, analysis of residues. Artificial Intelligence techruques.

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Current problems in this approach are to deal with the dynamic of the process and to mtegrate available models.

Supervision is more and more imponant for a good management of complex systems. It includes at least:

Mao-machine coo,perarion

- Preventive maintenance - Diagnosis with the different steps: · detection · localisation · reconfiguration of the system and/or the contrOl

Man and machine have complementary abilities, then it is an usual tendancy nowadays to keep human operator in coordination with computers for the management of complex systems.

Preventive maintenance (Titli. Carriere. 1988)

Cenainlyan efficient interface between man ,and machine are Knowledge Based Syste"s. malnly expen systems.

Incidents are really costly on complex systems and a main goal of operators in charge with the system is to avoid these incidents by preve.ntive actions. For this, a general scheme can be (FIg. 2) 264

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Expert systems have given good results for offline diagnosis problems. When used on line. additional problems occur Linked to : - the quantity of information to deal with - the changes over the time of this information - the characteristics of this informallon (noisy data. absent data. suspect data. ...) - the need to integrate knowledge on the process (deep knowledge : flow diagram. graphical representation . mathematical model. generic knowledge. meta-knowledge ... ) and to validate this knowledge by examining : · consistency . contradiction · conformance with deep knowledge · completness ... - the explanation of the decision to operatOrs - the time response of the expert -system compatible (or not) with the dynamic of the process

the degree of belonging to a given set (fuzzy set) and taking values in the range 0 to 1. Classical fields of applications of fuzzy logic are : - decision miling methods - expen systems - signal and image processing - classification and pattern recognition - control and integrated autOmation of course Indeed fuzzy logic under the form of fuzzy controller can be used for direct control at the la yer I in the integrated automation hierarchy (Fig. I ) (see section ill· But fuzzy logic can be used too in all the "symbolic/declarative" level. reducing the number of rules to take into account, then reducing some real time problem during implementation . Fuz.zy logic is also very well suited for the (numericaVsymbolic) conversion and vice-versa. for communication between symbolic and al gorithmic levels and between man and machine in general.

- the con version between qt; ali tative (sy mbolic) and quantitatlve (algonr nmlc ) re latlons and informations PotentiallOOls to tackle these problems are : - temporal logics - non monotOnic logics - qualitative physics - fuzzy reasoning. etc ...

FU2ZY LOOIC AND FUZZY CONTROLLER RJR DIRECr CONTROL

The basic fuzzy controller

Despite these interrogations or open problems under consideration by Artific ial Intelligence speclallsls . knowledge en gineenng offers. from this day .on. efficient tools to deal with particular and difficult problems for which mathematical models and algonthmic solutions are not available.

Fuzzy logic was first applied to develop fuzz y controller by Mandani (1974J uSing rules like th is: if and then Premises and conclusion in each ru .:: are defined with linguistic variables :

The inte~rated control structure in teans of the nawn:: of calculys at ctiffen::m levels

If and then .

with respect of the nature of the tasks realized at different levels. we can construct the following diagram

Observing a given situation on the process to be controlled, the rules are fired referring to a fuzzy inference scheme (generalized modus ponens). the conclusion of the fired rules are combined to get a fuzzy control which is finally convened into a continuous control variable to anack the proces.

Symbolic (declarati ve) task

Numericall symbolic _ conversion

The general structure of the feedback with fuzzy controller is given bellow:

... Symbolic/numerical conversion Algcrithmic (procedural) task

AID conversion

D/A conversion Fig. 4 - Fuzzy controlled process

Complex process

Details of the fuzzy controller are :

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Fig. 3 - Algorithmic and symbolic tasks in integrated automation Inqodyction .of the fuzzy the wtewted AY'omagon

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Fuzzy logic has been introduced by Zadeh (1965) to deal with uncertainty and qualitative information. manipulating linguistic variables defined by their membership function expressing

Fig. S - Fuzzy controllers 265

Combined use of fuuy IQ~c and other techniQues Automatic control and fuUY lo~c The automatic control field has to its disposal a set of efficient algorithmic procedures which have to be completed. improved when used in bad conditions (far from linearity conditions. with constraints on state and control •...). Two possibilities elUst to do this. in a hierarchical structure or in a parallel struCture. FuZZY supervision of "classic" controller in a hierarchical manner (lilce in adapti ve control)

Fig. 8 • Adaptation of a fuzzy controller through the use of neural networks Different interesting problems arise in this approach. · systematic conversion fuzzy rules····> neural networa

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Fig. 6 . Fuzzy supervision of a classical controller

· updating weighting parameters in the equivalent neural network, using. eventually, techniques issued from the Automatic control field (parameters estimation techniques. Kalman fll tering).

The problem is to design the rules of supervision and to study the perfonnances of the overall system .

APPUCA nON OF FUZZY CONTROL

Parallel combina tion of fuzzy controller and classical controller

We have developped a lot of work for the evaluation of fuzzy controllers :

Near set point. lineansed models can be obtained for the controlled process and used to design efficient "classical " controllers through different techniques in automatic control.

· by simulation on a classical example of servo·motor (Bovene 1991) · on an international benchmark (Boverie 1992)

Far from steady state operating conditions. fuzzy controller will show probably more robustness. Then it is cena in ly interesting to combine ad vantages of both approaches in a single loop. The transition between one mode of control to another being smoot!l and perhaps ... fuzzy itself.

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· on real systems · on a motor alternator group (Titli 1991) · on automotive systems (Boverie 1992) Details on these applications will be glVen dWlng oral presentation. The results show surprising properties of robustness associated to an easy design of fuzzy controllers. Another applications can be classified in :

Fig. 7 . Parallelism between fuzzy and conventional controllers

• process control · transponation systems · mobile systems · domestic appliances • audio-video systems • etc ...

ComDlemenw:y use of fuzzy lo~c and neural ~

It is well known that fuzzy logic is indicated to tackle with uncertain ty and qualitative infonnation while neural networks have big capabilities of learning. This can be used for the design of adaptive·fuzzy controller or learning·fuzzy controller. depending on the degree of adaptation desired. An approach to do this is to conven the initial set of rules into a neural network and then to use real data on line. to update the weighting factors in the neural networX.

CONo...USION Fuzzy control has got a big success in different fields of applications. for direct control and supervisory control but essentially on SISO problems. Cenainly more effon has to be put on these techniques to tackle MIMO problems dealing with coupling between variables and introduc!lng hierarchy in the control structure.

The last step is to reconven the neural network into a new set of rules with new membership functions. and perhaps new rules.

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REFERENCES AstrOm KJ. (1991) . Intelli~ent control Preprints of the ECC91. Grenoble. July.

Singh M.G .• Titli A. (Edjtors) (1979). Handbook of large scale systems engineering applications. NOM Holland Publishing CompanY, Amsterdam.

Bemussou 1.• Titli A. (1982). Interconnected dynamical systems : stability decomposition decentralisation. NOM Holland, Amsterdam.

Titli A. (1975). Commande hierarchisee et optimisation des processus complexes. ~. Paris. Titli A. (1987). Complex systems methodology . Systems and Control Encyclopedia Pergamon illll. Oxford, vo!. I. pp. 687 -704.

Boverie S .• Demaya B., Ketata R.• Titli A. (1992) Performance evaluation of fuuy controller : IFAC Symposium on Intelli~ent components and InsQJJmep[s for Control apphcatlons . Malaga. Spain. May 20-22.

Titli A.• Carriere 1.C. (1988) . Estlmallon of continuous parameters with low pass fill er operator . Internal repoo. LAAS-C:-;RS. Toulouse.

Boverie S .• Demaya B.. Le Quellec 1.M .. Titli A. (1992) Contribution of fuuy logic control to the improvement of modern car performances. ~ Symposium on Arti iici allnte !li gence in Real time ~ . Delft, The Netherlands. June 16-18.

Ti tl i A. et al . (1979). Analyse et commande des systemes complexes . Editi ons CEPA Dl' ES, Toulouse.

Boverie S.• Demaya B.• Titli A. (1991) Fuzzy logic control compared with other automatic control approaches - 30th IEEE·CDE Brighton (UK). December 11-13.

Titli A.. Ketata R. : Design and application of fuuy algonth for the speed contro l of a motoralternator group. 13th IMACS C o n~re s s on computa tion and applied mathematlcs. Dubhn. July 22-26. 1991.

Mandani E.H. (1974) . Appl ication of fuzzy algorithm for control of simple dynamic plant Proc.IEEE.!21.!585 . 1588.

Tit!i A.• Singh M.G. (Editors ) (l980) : Large scale systems theory and applications . Pergam on Errn. Oxford.

Schmidt G .. Singh M.G.• Ti tli A.. Tsafeslas S. (Edjtors) (1984). Real time control of large scale systems. Springer Verlag.

Trave-Massu yes L .. Missier A.. Piera N. (! 990). Qualitative models for Automatic Control Process Supervision - 11th IFAC World conness. TallilUl.

Singh M.G .• Titli A. (1978) . Systems decomposition. optimisation and control Pergamon Press Oxford.

Trave-Massuyes L., Titli A., Tarras A. (1989). Large Scale Systems : decentralization. structure constraints and fixed modes - Spnnger yerlag. Berlin.

Singh M.G .• Titli A. (Editors) (1978). Control and management of industrial integrated systems. Per~amon Press. Oxford.

Zadeh L.A. (1965). Fuzzy sets, Information and Control - p. 330. 353.

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